Phase diagrams of PEG1000,1500,2000,4000,6000 + lithium citrate + water ATPSs, and the partitioning of salbutamol at T = 298.15 K

Salbutamol is a drug used to treat the pulmonary diseases by ameliorate the medium and large airways in the lungs. Partitioning of salbutamol drug on the aqueous two-phase systems (ATPSs) of PEG1000,1500,2000,4000,6000 + trilithium citrate + water was determined at T = 298.15 K. The effect of molecular mass of polymer (MMP) on the binodal and tie-line compositions were studied. Results showed that the biphasic area was extended as the MMP was increased. The salting-out ability were quantified using the Setschenow model, and the binodal curves were modeled by a nonlinear 3-parameter equation. Furthermore, electrolyte Wilson along with the osmotic virial models have adequately been implemented to fit the tie-line compositions. Also, the studied ATPSs were implemented to study the partitioning of salbutamol drug on the salt-affluent and polymer-affluent phases. It is observed that, ATPSs of PEG1000 is premium to extract the salbutamol to the polymer-affluent phase, where, the ATPSs of PEG6000 is more favorable to extract the drug to the salt-affluent phase.

www.nature.com/scientificreports/ or salt solution), and water were determined, and the binodal curve compositions were calculated. During this process, the water circulator-thermostat (Fanavaran Sahand Azar Co., model No.12 uc5000s, Iran) was set at T = 298.15 K. The temperature of the double-wall glass cell was further controlled using a normal thermometer with the precision of 0.1 K. The repetitive experiments were continued for 5 times for each desired mass of the polymer, and the mean standard uncertainty (u) of the mass fractions (w) was found to be u(w) = 0.0009. The tie-line samples were prepared by mixing appropriate amounts of PEG stock solution (40 to 60% w/w), and salt solution (~ 35% w/w), and double-distilled deionized water in the closed glass containers to obtain the total solution of ~ 30 g. The PEG total mass fraction in the stock solutions was fixed at ~ 15% w/w for PEG 1000-4000 , and 25% w/w for PEG 6000 . Also, the mass fractions of the salt were selected such that the final solution be in the biphasic region. The thermostat was set to the temperature of T = 298.15 K, the closed containers were immersed in the thermostated water for at least 72 h, and the mixture was allowed to achieve the thermodynamic equilibrium. Then, the polymer-affluent phase was separated by a long-needle syringe from the salt-affluent phase. Also, the remaining solution of the bottom-phase was depleted into separate vessels, and the mass of the top and bottom phases were measured to calculate the composition of each component in each phase from the gravimetric analysis method proposed in our previous work 13 .
Following our previous work 13 , the mass-fractions (w) of the components in both phases were determined by numerical solution of the subsequent set of equations: In these relations, w 1 , w 2 , and w 3 are the mass fractions of PEG, salt, and water, respectively. Also, "top", "bot", and "mix" superscripts referred to the polymer-affluent, salt affluent, and the stock solutions of the primary solution, respectively. Equations (1) and (2) are the mathematical representation of the binodal curves, which is presented for polymer-affluent region (i.e., Eq. (1)), and the salt-affluent region (i.e., Eq. (2)). Moreover, Eqs. (3) and (4) are derived from the thermodynamical lever-rule, and the remaining equations shows the mass balance of the coexisting phases. For each stock solution, the tie-line compositions repeated at least 3 times, and the reported data are the arithmetic average of the obtained results. The mean of the standard uncertainty (u) for the calculated mass fractions (w) of the tie-lines was estimated to be u(w) = 0.0014. The separated top and bottom phase samples were kept in closed glass containers to be used as blanks in determination of the concentration of salbutamol.
The designed tie-lines were also used to study the salbutamol partitioning in two-phases of the PEG + trilithium citrate + water ATPSs. For this purpose, the tie-lines with concentrations equal to the previous step were prepared and ~ 0.003 g of salbutamol was added into each sample. The samples then were settled in the thermostated bath at the temperature of T = 298.15 K for at least 48 h, and then, the two phases were separated. Consequently, the UV-visible absorption spectrophotometry was implemented to determine the salbutamol www.nature.com/scientificreports/ concentration in top and bottom phases. Different chemicals with different concentrations of polymer or salt have different wavelengths in UV-visible spectra. So, different standard calibration curves of salbutamol (0-10 ppm) were prepared for each drug-containing-phase using the remaining values of each individual phase samples kept from the previous section. To measure the absorbance of salbutamol in each sample, a quartz cell with the cell-length of 1 cm was used in UV-visible spectroscopy (Biochrom company, model no. Libra S12, U.K). The measurement was made at λ max = 428 nm. Each sample was diluted to be in the range of the calibrations curve, and the polymer and salt affluent salbutamol-free solutions, remaining from previous step, were diluted with the same dilution factor, and used to prepare the blank solution.
The partitioning coefficient, D, the extraction efficiency percent, E%, and the separation coefficient, R, were calculated from the following equations: where C refers to the salbutamol concentration (ppm), and m is the total mass of the salbutamol-free polymerand salt-affluent phases.

Results and discussion
The measured binodal and tie-line concentration. The measured binodal curves of the ternary system composed of PEG 1000,1500,2000,4000,6000 + trilithium citrate + water at T = 298.15 K were given in Table 2, and were shown in Fig. 1. The expansion of the biphasic area resulting from the increase of the MMP is obvious from Fig. 1. The mass fractions of the PEG and salt for the measured tie-lines were reported in Table 3. Moreover, the tie-line length (TLL) and slope (TLS) were computed using Eqs. (10) and (11): In these equations, 1 and 2 subscripts refer to the PEG and trilithium citrate, and, the "top" and "bot" superscripts show the polymer and salt-affluent regions, respectively. The estimated values of the TLL and TLS of the tie-lines were reported in Table 3. The raising of the biphasic area was clearly observed from TLL values; however, there is not a clear trend for TLS.
The TLL and TLS of the studied tie-line were graphically shown as a function of the mass fraction of the salt in stock-solution in Fig. 2a, and b, respectively. It is obvious from Fig. 2a that, as the MMP was increased, the TLL was increased, which confirms that the surface area of the biphasic area was enlarged.
In other words, by increasing MMP, and therefore the chain length of the polymer, the hydrophobic interactions between the polymer chains were increased, and therefore, the tendency of the polymer chains to separate from the aqueous solution as an independent phase was increased. So, the tendency of the PEG + trilithium + water system to form a biphasic system was increased.
Correlation of the binodal and tie-line composition. One of the major parts of any thermodynamics study is the modeling of the measured data. In fact, a desirable model can provide a mathematical description of the experimental results, which can be used in further studies more precisely. So, several acceptable models have been applied in this work to correlate the experimental tie-line data, Indeed, Setschenow 18 , osmotic virial 42 , and the electrolyte-Wilson 39 models were applied to model the thermodynamics of the studied ATPSs.
The experimental binodal curves were fitted with a 3-parameter non-linear Merchuk equation 25 : The parameters of this equation (i.e., a, b, and c) were obtained from the non-linear least-square fitting of the mass fraction of PEG (w 1 ) and trilithium citrate (w 2 ). The experimental binodal data were fitted with Eq. (12) by minimizing the least squares errors of the following objective function (OF), In which, w 1 , exp, i is the i'th experimental mass fraction of the PEG at desired binodal curve. In minimization of Eq. (13) the nonlinear Levenberg-Marquardt optimization algorithm was used. The fitting results, together with the statical analysis of the goodness of fit (i.e., average absolute deviation (AAD%), standard deviation SD, and the coefficient of determination R 2 ) were presented in Table 4. The adequate consistency between the correlated the measured binodal data can be inferred from the results reported in Table 4.
The solute-solvent interactions may change the structure of the solvent. The hydrogen-bonding between the solute and water is the principal interaction impress the solvent structure. Some solutes can increase the www.nature.com/scientificreports/ intermolecular interaction between the water molecules, and therefore, water molecules are aligned next to each other in a more regular structure; these solutes are kosmotropic salts 43 . The dissolution of some other solutes may also result in a disordered hydrogen-bonding structure of the water network. The second class of the solutes are Chaotropic salts 44 . Moreover, the dissolution of kosmotropic salts in aqueous solution at a critical concentration can salting-out the other compounds form the aqueous solution.
The salting-out capability of PEG + salt + water ATPS has been investigated in the present work using the Setschenow-type model 13,45 : where k s and k 0 are fitting parameters, and the C 1 and C 2 refers to the molarity of PEG and tri-lithium citrate, respectively. Moreover, top and bot superscripts refer to the PEG and trilithium citrate-affluent regions, respectively. Furthermore, k s is a constant repeatedly used in the literature 13 to quantify the salting-out capability of the ATPSs. So that, the more the k s the more the two-phase formation tendency of the ATPS. Calculated k s values  www.nature.com/scientificreports/ were reported in Table 5. The enhancement of the salting-out coefficient, k s , with increasing the MMP, and the salting-out ability of the studied ATPSs is obvious from the Table 5.
Liquid-liquid equilibria of PEG 1000,1500,2000,4000,6000 + trilithium citrate + water was also modeled using the virial expansion of the chemical potential (µ) 42 . The following relations were applied to estimate the µ of the PEG (µ 1 ) and trilithium citrate (µ 2 ): In these relations, the standard state of µ displayed as µ • i , i = 1, 2 , whereas, 1 and 2 subscripts refer to the PEG and electrolyte. Also, β ij represented the interaction of i and j component. The chemical potential of water (µ 3 ) can also be derived from the Gibbs-Duhem relation as follows: The fitting parameters (i.e., β ij with i, j = 1, 2, and 3) were obtained by minimizing the following objective function, and are reported in Table 6.
In Eq. (18), subscribes of "exp" and "cal" are experimental and calculated mass fractions, respectively; p indicates a phase (top-phase or bottom), of l'th tie-line, and j refers toe the PEG, salt, or water. Also, the condition of equal chemical potential for all components (i.e., µ top i = µ bot i , where i = 1, 2 and 3) has been applied to establish the thermodynamic equilibria, and to correlate the tie-line data with the model 46 .
The experimental compositions of the measured tie-line lines are compared with the calculated concentration from the osmotic virial model in Fig. 3. The estimated parameters of the model were also reported in Table 6. An acceptable fitting results can be inferred from Fig. 3 and Table 6.
The hydrophobic interactions and the solvent can control the properties like virial coefficients and volume of solute in solution phase. Zafarani-Moattar et al. 47 showed that the infinite dilution apparent molal volume ( V ∞ ϕ,m ) of PEG is independent of the molecular mass of the polymer, and the value of V ∞ ϕ,m ≃ 37.0 cm 3 /mol was reported for PEG 2000 and PEG 4000 at T = 298.15 K. The limiting V ∞ ϕ,m = 149.35 at T = 298.15 K for trilithium citrate in aqueous solution was reported by Devi and coworkers 48 . However, they also found that, the V ∞ ϕ,m values were decreased in aqueous solution by increasing the concentration of the [Emim][HSO 4 ] ionic liquid. They also concluded that, the hydrophobic-hydrophobic and ion-hydrophobic interactions are more dominant than the hydrophilic-hydrophilic and ion-hydrophilic interactions in aqueous solutions. The increasing behavior of the polymer-polymer (β 11 ) and polymer-salt (β 12 ) virial coefficients with increasing the molecular mass of polymer (MMP) can be seen from Table 6, which is more obvious for β 11 . Whereas, the salt-salt (β 22 ) virial coefficient is almost independent of molecular mass of PEG. In other words, it seems that, by increasing the MMP, especially in the case of PEG 4000 and PEG 6000 , the polymer-polymer interactions were increased more substantially than the PEG-salt interactions, which motivated the PEG particles to exclude from the rest of the solution as an independent phase. In other words, this simple model provides a microscopic view of the molecular interaction. By increasing the MMP, and therefore, increasing the number of the monomers of the PEG, the probability of www.nature.com/scientificreports/ monomer-monomer interactions was more likely, compared to the water-monomer and ion-monomer interactions. Therefore, the system is more favorable to form a biphasic ATPS. This conclusion agrees with the experimental results of this work, whereas, the two-phase formation affinity of the studied ATPSs were increased by increasing the molecular mass of PEG. Electrolyte-Wilson model was extended for the aqueous systems of polymer + electrolyte + water systems by Sadeghi et al. 39 All equations, definitions and information about chemical potential, activity coefficients and phase equilibrium condition of this model were demonstrated in our previous works 13,41 , and only the results of the tie-line correlation for ATPSs composed of PEG 1000,1500,2000,4000,6000 + trilithium citrate + water of data were reported in this work. Furthermore, the dielectric constant, D s , molar volume, V s , and the estimated number of the segments for each polymer (i.e., r 1 ) were reported in Table 7.
The calculated parameters of the e-Wilson model were reported in Table 8, and the experimental and correlated results were compared in Figs. 4, 5, 6, 7 and 8. The excellent concurrence of the modeled and experimental tie-lines is obvious from Table 8 Table 3, and were shown graphically in Fig. 9. Table 3. Experimental tie-line mass factions (w) for PEG 1000,1500,2000,4000,6000 (1) + trilithium citrate (2) + water (3) system at T = 298.15 K, and P = 101 KP, along with the tie-line length (TLL), and tie-line slop (TLS). The measured partitioning coefficient (D obs ), the extraction efficiency percent (E%), and the separation coefficient (R) of the salbutamol in the studied tie-lines were also reported. Standard uncertainties, u, are u(T) = 0.1 K, u(w) = 0.0013, and u(P) = 5 kPa. www.nature.com/scientificreports/ Different MMPs (i.e., MMP = 1000, 1500, 2000, 4000, and 6000) were used in the investigated ATPS for salbutamol partitioning. According to Fig. 9a, the salbutamol concentration in the polymer-affluent phase was superior than the bottom phase for PEG 1000 and PEG 1500 . So that, the maximum value of D = 2.67 was observed in PEG 1000 . This value is approximately equal in both phases for PEG 2000 and PEG 4000 , and the average of the D is 1.15 and 0.96 for PEG 2000 , and PEG PEG 4000 , respectively. In PEG 6000 , the drug was concentrated in the saltaffluent phase, i.e., D is ~ 0.5. Therefore, at T = 298.15 K the lower MMP of PEG resulted in the higher partitioning coefficient, and polymers with higher molecular mass have more acceptable outcomes for drug extraction in aqueous solvents. Also, the standard deviations of the obtained D values are 0.1, 0.15, 0.04, 0.09, and 0.03 for ATPSs composed of PEGs with MMP = 1000, 1500, 2000, 4000, and 6000, respectively, which, confirm that D is independent of TLL. More precisely, only in the case of PEG 1000 , the D was slightly decreased by increasing the TLL, and inversely, for PEG 2000 an almost increasing behavior of D with an increase of the TLL was observed.  www.nature.com/scientificreports/ The efficiency (E%) as function of separation coefficient, R, and TLL were shown in Fig. 9b, and d, respectively. In all cases, other than PEG 6000 , the E% values are lower than 50%, and the efficiency was decreased by increasing the MMP until 4000. The separation ability as function of TLL, as shown in Fig. 9c, also demonstrate that, other than PEG 6000 , the R values are lower than 1.0, which is almost increased by increasing the MMP.
The inconsistence behavior of PEG 6000 is due to the more tendency of PEG 6000 to form a biphasic system. Indeed, from Fig. 9c it can be inferred that, the mass of the polymer-affluent phase is higher than the salt-affluent phase. In other words, PEG 6000 can catch more water molecules from the stock solution in competition with the Table 5. Results of the fitting of the experimental tie-line compositions with the Seteschenow-type model (i.e., Eq. 14) for PEG 1000,1500,2000,4000,6000 (1) + trilithium citrate (2) + water (3) system at T = 298.15 K. R 2 is the coefficient of determination for linear relation of ln C    www.nature.com/scientificreports/ ionic components, compared to the other polymers. However, in all other cases the mass of salt-affluent phase is more than the top-phase, due to the more water molecules cached with the ionic components when contest with the polymer chains.

Conclusion
In this paper, LLE phase diagrams for the systems of PEG 1000,1500,2000,4000,6000 + trilithium citrate + water at T = 298.15 K were reported. The binodal curves were collected and fitted susccesfully by the Merchuk equation. Setschenow-type model were applied to study the salting-out capability. It was found that, salting-out parameter (k s ) was boosted with enhancement of MMP. In other words, the tendency of the salt-affluent phase was intensified to adopt the H 2 O moleculs with increasing the length of the polymer chain. Furthermore, osmotic virial and electrolyte-Wilson models were implemented for thermodynamical modeling of the phase equilibrium. It was found that, there is a direct relationship between the MMP, binodal curves extent, and the tie-line length. So that, the more the MMP the more the two-phase extent of the phase diagram. Besides, partitioning coefficient (D) of salbutamol was measured in the studied ATPSs. According to the obtained data, it can be claimed that, the partioning coeffeicnet (D) of salbutamol was decreased with increasing the MMP. PEG 6000 with minimum amount of D = 0.47, and high efficiency parcentage of 72% was appropriate for drug dissolution in the salt-affluent phase, and PEG 1000 is better to transfer the salbutamol molecules to the polymer-affluent phase. Therfore, partitioning of salbutamol can be controlled by changing the MMP in PEG + trilithium citrate + water ATPS.  www.nature.com/scientificreports/